However, if no x satisfies the equation or more than one x does—that is the solution is not unique—the problem is said not to be well posed.
In the line(source: Wikipedia) above it uses "more than one does", but logically and intuitively it should be "more than one do" since "more than one" means two or more, then it is plural. I have tried my best to interpret it as it is, but hardly can I convince myself to make "more than" collocate with "does" as an adv., which may only make it make sense.
Your logic is impeccable; unfortunately the convention is to use "more than one does" even if it's technically a plural.
Digging deeper, I found this from the American Heritage Dictionary
When a noun phrase contains more than one and a singular noun, the verb is normally singular: More than one editor is working on that project. More than one field has been planted with oats. When more than one is followed by of and a plural noun, the verb is plural: More than one of the paintings were stolen. More than one of the cottages are for sale. When more than one stands alone, it usually takes a singular verb, but it may take a plural verb if the notion of multiplicity predominates: The operating rooms are all in good order. More than one is (or are) equipped with the latest imaging technology.
Again, I'd say this is more convention than rule, but it's still a good idea to follow.
The basic structure, you would want to note when such doubt arises, is what subject is the verb describing. Here, In conditional phrase under question, x is the subject- satisfying of the equation by x. So, the question is whether or not, x satisfies the equation? Therefore, only set of option you are left with is x does or x does not. Both are the singular form of verbs.
